Question: Evaluate $(a^b)^a - (b^a)^b$ for $a = 2$ and $b = 3$.
Solution: We have  \begin{align*}
(a^b)^a - (b^a)^b &= (2^3)^2 - (3^2)^3\\
&=8^2 - 9^3\\
&=64-729\\
&=\boxed{-665}.
\end{align*}